Then,
for every subset Y1 of Y, a rule of the form Y1 ?‡’ Y2 is generated if its confidence ?‰?
minconf (a user-defined threshold).
Since the introduction of Apriori, a variety of approaches to the problem of association
rule mining has been proposed. The main objective of most of them is to
improve the efficiency of the basic method, while the key difficulty is the potentially
large number of frequent itemsets (FIs). To reduce the size of the FI set, some
studies were conducted on frequent closed itemsets FCIs (Pasquier, Taouil, Bastide,
Stumme, & Lakhal, 2005; Wang & Karypis, 2003; Zaki & Hsiao, 2002). A frequent
itemset X is closed if there exists no proper superset Z of Y with supp(Y)=supp(Z).
In other words, any itemset has the same support (i.e., is frequent) as its closure. In
a dual way, a tidset X is closed if there exists no proper superset U of X such that U
and X have the same set of items.
In the closed itemset framework, some studies were concerned with the generation
of nonredundant sets of association rules (Pasquier et al., 2005; Pfaltz & Taylor,
2002; Valtchev, 2002b) where Y1 is a generator, that is, a minimal subset of Y such
that its closure is equal to Y.
The following is a summary of the key results from concept lattice theory (Ganter
& Wille, 1999), which provides the basis of our approach towards the generation
of frequent closed itemsets and association rules as well as manipulation of DM
output and visualization using a nested structure.
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